ProxNet:
Similar to [1]}, the proximal operators for \(\mathbf {z}_T\)  and \(\mathbf {z}_R\)  in Eq. (REF ) and (REF ) are represented by two deep convolutional networks \(\text{ProxNet}_{\mathbf {\theta }_{\mathbf {z}_T}}(\cdot )\)  and \(\text{ProxNet}_{\mathbf {\theta }_{\mathbf {z}_R}}(\cdot )\) 
whose parameters are learned from the training dataset to well capture the prior information.
The updating rule for \(\mathbf {z}_T\)  and \(\mathbf {z}_R\)  can be therefore expressed as:
\({\left\lbrace \begin{array}{ll}\nabla f(\mathbf {z}_T^{(k)}) = - \mathbf {K}_T^{(k)} \otimes ^{T} \left( \hat{\mathbf {T}}^{(k)} - \mathbf {D}_T^{(k)} \otimes \mathbf {z}_T^{(k)} \right), \\\mathbf {z}_T^{(k+1)} = \text{ProxNet}_{\mathbf {\theta }_{\mathbf {z}_T}} \left( \mathbf {z}_T^{(k)} - \nabla f(\mathbf {z}_T^{(k)}) \right), \\\end{array}\right.}\) 
\({\left\lbrace \begin{array}{ll}\nabla h(\mathbf {z}_R^{(k)}) = - \mathbf {K}_R^{(k)} \otimes ^{T} \left( \hat{\mathbf {R}}^{(k)} - \mathbf {D}_R^{(k)} \otimes \mathbf {z}_R^{(k)} \right), \\\mathbf {z}_R^{(k+1)} = \text{ProxNet}_{\mathbf {\theta }_{\mathbf {z}_R}} \left( \mathbf {z}_R^{(k)} - \nabla f(\mathbf {z}_R^{(k)}) \right),\end{array}\right.}\) 
